Equation 123 · Part 2 · The Bend an Elevator Cannot Fake

Symbol y_1

y_2 - y_1 = \phi_{,zz}\,h^2 + O(h^4).

y_1

What this part means

$\sqrt2$ \, $\sigma_y$ .

Its job in the formula

$y_1$ is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol y_1Article meaning

Where the article explains it

The combined noise on the independent-edge difference $y_2$ - $y_1$ is $\sqrt2$ \, $\sigma_y$ .

The passage around this formula

An exact analytic evaluation, not a simulation, fixes the scale this actually requires. Take three clocks stacked vertically at heights -h , 0 , and +h near Earth’s surface, giving two edges $y_1$ = $\phi(0)$ - $\phi(-h)$ and $y_2$ = $\phi(h)$ - $\phi(0)$ . Their difference is an exact finite-difference identity up to a Taylor remainder of order $h^4$ : $y_2 - y_1 = \phi_{,zz}\,h^2 + O(h^4)$ . For Earth modelled as a point mass, $\Phi(r)$ = -GM/r gives a radial second derivative of magnitude 2GM/ $R^3$ and, since $\Phi$ is…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

[15] Physical Geodesy ↗

These citations provide research context; check each source for the exact claim it supports.